Free number software for linux

The Mango Library is a Java library consisting of a number of iterators, algorithms and functions, loosely inspired by the C++ Standard Template Library.
Enhancements:
- This release adds a further two iterators.

Math::BaseArith is a Perl extension for mixed-base number representation (like APL encode/decode).

SYNOPSIS

use Math::BaseArith;
encode( value, base_list );
decode( representation_list, base_list );

The inspiration for this module is a pair of functions in the APL programming language called encode (a.k.a. "representation") and decode (a.k.a. base-value). Their principal use is to convert numbers from one number base to another. Mixed number bases are permitted.

In this perl implementation, the representation of a number in a particular number base consists of a list whose elements are the digit values in that base. For example, the decimal number 31 would be expressed in binary as a list of five ones with any number of leading zeros: [0, 0, 0, 1, 1, 1, 1, 1]. The same number expressed as three hexadecimal (base 16) digits would be [0, 1, 15], while in base 10 it would be [0, 3, 1]. Fifty-one inches would be expressed in yards, feet, inches as [1, 1, 3], an example of a mixed number base.

In the following description of encode and decode, Q will mean an abstract value or quantity, R will be its representation and B will define the number base. Q will be a perl scalar; R and B are perl lists. The values in R correspond to the radix values in B.

In the examples below, assume the output of print has been altered by setting $, = and that => is your shell prompt.

Math::Numbers is a Perl module that contains methods for mathematical approaches of concepts of the number theory.

SYNOPSIS

use Math::Numbers;

my $a = 123;
my $b = 34;

my $numbers = Math::Numbers->new($a, $b [, ...]);

print "They are coprimes (relatively primes)!n" if $numbers->are_coprimes;
print "The greatest common divisor of these at least two numbers is ", $numbers->gcd;

my $number = Math::Numbers->new($a);

print "It is prime!n" if $number->is_prime;

my @divisors = $number->get_divisors;

print "$a is divisor of $b!n" if $number->is_divisor_of($b);

Math::Numbers is quite a simple module on matters of programming. What its interesting is the focus and approach it is intended to be made from the Number Theory basis for Perl beginners (like me) and also for young mathematicians (like me).

The normal topics of Number Theory include divisibility, prime numbers (which is separately intended to be covered by Math::Primes), congruences, quadratic residues, approximation for Real numbers, diophantine equations, etc. and all this is intended to be convered by the module on the concept on getting and setting values and also retriving the proof methods.

METHODS

new

# Some methods require more than only one argument.
my $numbers = Math::Numbers->new($p, $q, ...);

# Some methods require only one.
my $number = Math::Numbers->new($p);

Create a Math::Numbers object. Note that some of the methods will require objects created with only one or a defined numbers of arguments.

gcd
my $gcd = $numbers->gcd;

Calculation of the Greatest Common Divisor. This is made by two different methods which are described below: Blutos algorithm and Euclidean algorithm: The former is used when computing GCD for more than two integers; the latter is used when getting the GCD for two numbers to improve speed. See below for information on each.

Bluto_algorithm

You will mostly not require to call this method, but directly gcd(). Blutos algorithm uses a brute force calculation used by mathematicians to get divisors and then GCD also called Primality Test. Bluto takes some spinaches stolen from Popeye and starts dividing m all the way through 2 to m/2.

Euclidean_algorithm

Euclid rocks. I have a very nice Budgerigar (http://en.wikipedia.org/wiki/Budgerigar) called the same in honor of him (have to upload a pic of him).

As of now, this algorithm is only computed on two integers. From the Wikipedia entry: Given two natural numbers a and b: check if b is zero; if yes, a is the gcd. If not, repeat the process using (respectively) b, and the remainder after dividing a by b. This is exactly what our method does.
is_divisor_of

print "Yes, $p is divisor of $a...n" if $number->is_divisor_of($a);

Lets see if the number from the object is a divisor of $a, which means that the division $number/$a will return an integer (not necesarily a natural). If it does, itll return 1; 0, otherwise.

get_divisors
my @divisors = $number->get_divisors;

What are the divisors of the number brought by the object? This only includes the Natural numbers.

is_prime
print "$p is not prime!n" unless $number->is_prime

Returns 0 or 1 if the number from the object is prime or not, respectively. This method uses the, a bit slow, primality test.

are_coprimes
print "They are coprimes because their GCD is 1!n" if $numbers->are_coprimes;

Are the numbers from the object coprimes (relatively primes)? This means, the GCD is 1; (a, b, c, ...) = 1. Returns 1 or 0.

mrtg-misc-probe probes different system features for mrtg to graph.
Currently it can probe:
- percent usage of disk space and inodes for UFS filesystems
- percent usage of disk space for VxFS filesystems
- incoming and outgoing mail messages on sendmail mail server
- total size of mail messages sendt and received on sendmail mail server
- network delay using NTP peers/servers
- number of ClearCase vobs and views
- number of available and used ClearCase and MultiSite licenses
- number of active and disconnected sessions of a Citrix Metaframe server
- number of reachable hosts in a given network range
- network device reachability (ping success)
Enhancements:
- New probes: ctxmf - number of active and disconnected Citrix Metaframe sessions; hostcount - scan given nmap-network-range and return number of hosts found.

Number::WithError is a Perl module that contains numbers with error propagation and scientific rounding.

SYNOPSIS

use Number::WithError;

my $num = Number::WithError->new(5.647, 0.31);
print $num . "n";
# prints 5.65e+00 +/- 3.1e-01
# (I.e. it automatically does scientific rounding)

my $another = $num * 3;
print $another . "n";
# propagates the error assuming gaussian errors
# prints 1.69e+01 +/- 9.3e-01

# trigonometric functions also work:
print sin($another) . "n";
# prints -9.4e-01 +/- 3.1e-01

my $third = $another ** $num;
print $third. "n";
# propagates both errors into one.
# prints 8.7e+06 +/- 8.1e+06

# shortcut for the constructor:
use Number::WithError witherror;
$num = witherror(0.00032678, [2.5e-5, 3e-5], 5e-6);
# can deal with any number of errors, even with asymmetric errors
print $num . "n";
# prints 3.268e-04 + 2.5e-05 - 3.00e-05 +/- 5.0e-06
# Note: It may be annyoing that they dont all have the same
# exponent, but they *do* all have the sam significant digit!

This class is a container class for numbers with a number of associated symmetric and asymmetric errors. It overloads practically all common arithmetic operations and trigonometric functions to propagate the errors. It can do proper scientific rounding (as explained in more detail below in the documentation of the significant_digit() method).

You can use Math::BigFloat objects as the internal representation of numbers in order to support arbitrary precision calculations.

Errors are propagated using Gaussian error propagation.

With a notable exception, the test suite covers way over ninety percent of the code. The remaining holes are mostly difficult-to-test corner cases and sanity tests. The comparison routines are the exception for which there will be more extensive tests in a future release.

KWC application is a key width calculator.

Key Width Calculator (KWC) is a simple utility that calculates how many bits are required to represent specified number of combinations.

Run it without command line options for brief help message. Command line options are converted to long integers under strtol(3) conversion base 0, ie you can mix octal, decimal and hexadecimal numbers. These integers are multiplied to make required number of combinations. Key coverage data are also calculated.